Ground-based observations of geocoronal Balmer &agr; (H&agr;) emission were performed with a large-aperture, dual-etalon Fabry-Perot spectrometer at a resolving power of about 25,000, which clearly isolates the geocoronal emission from galactic and zodiacal light backgrounds. During each observing night, observations were conducted alternately between two directions, one at 60¿ zenith distance in the sun's azimuth and the other in the antisolar direction, to compare the emission primarily from single scattering of solar Lyman &bgr; with that primarily from multiple scattering, and to evaluate the intensity variations over various time scales. Accurate intensity calibration was obtained by observing astronomical photometric standard sources on each night of observation. The morning enhancement of the observed H&agr; intensities in both directions is 10%. Assuming single scattering dominates, the observed intensity variation seems difficult to reconcile with the standard diurnal variation model which implies an increase at mid-latitudes of about 30% in the exobase hydrogen density between the evening period and the post-midnight period. In contrast to the standard diurnal variation model, some satellite measurements indicate a morning hydrogen trough in northern mid-latitudes, a result which appears to be consistent with the present measurements. Detailed radiative transfer calculations and model refinements are required to clarify the situation. Comparisons of H&agr; intensities observed on different nights with the same scattering geometry reveal a clear inverse relationship between the geocoronal H&agr; emission rate and the exospheric temperature based on the Jacchia 1977 model. Preliminary calculation shows this H&agr; intensity variation agrees with the results of several satellite experiments which found that the variation of the exobase hydrogen density with temperature is less rapid than that predicted by consideration of Jeans escape as the only hydrogen escape mechanism.